Other Approaches

There are various other approaches to controlling for the endogeneity of divorce. One rather common method is to use a continuous variable, time spent with a biological parent present in the household during childhood, as the treatment, instead of the binary divorce variable. Then one can compare children in the same family, who in the case of divorce, will have spent different amounts of time co-residing with the parent, and use fixed effects to control for family

unobservables. This approach is particularly popular in the sociological literature. Lang and Zagorsky (2000) and Sandefur and Wells (1997) are both good examples of this approach.

Sandefur and Wells (1997) find statistically significant effects of family structure on educational outcome, although the magnitude is lower than in studies that do not control for family

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unobservables. Lang and Zagorsky(2000) find that in most of their measures of adult economic well being, parental presence in childhood does not have an impact.

Lang and Zagorsky (2000) also compare the separation from parents caused by divorce (or other causes) to the separation caused by a more exogenous source of variation: death of a parent. Corak (2001) uses this approach as well. By comparing the two they attempt to show the degree of endogeneity of non-death separation. Lang and Zagorsky (2000) find almost no adult outcomes that are affected differently by death (except marital prospects for sons). Corak (2001) finds a high degree of endogeneity of divorce.

Another approach employs panel data to do pre-divorce and post-divorce analysis.

Painter and Levine (2000) use pre- and post-divorce measures of children’s economic,

educational and teenage fertility outcomes to determine if divorce and remarriage are causal or simply correlates. Using data from the National Educational Longitudinal Survey of 1988, they compare to-be-divorced children with to-remain-intact children before and at the end of their high school years. For the most part, they find that the individuals in to-be-divorced families were not significantly different in income to needs ratios or in eighth-grade test scores than their peers in families that remained intact. This leads the authors to conclude that their differences post-divorce are causal results of divorce.

Finally, there is the instrumental variable approach. Identifying a suitable instrument is extremely difficult. As stated by Jonathan Gruber (2000), “What is required to appropriately identify the impacts of divorce is an exogenous instrument that causes some families to divorce and others not, based on a factor independent of the determinants of their children’s outcomes.

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No previous study has been able to uncover such an instrument, making it somewhat hard to interpret causally this large literature.” (p. 10)

The instrument that is most often relied upon, however, is the adoption of unilateral divorce, or occasionally no-fault divorce. Unilateral divorce laws allow a divorce to take place even if one spouse objects to the divorce. These laws were enacted by a majority of states during the 1970’s and early 1980’s and so they supply a source of seemingly exogenous variation.⁶ (No-fault laws refer to either no-(No-fault divorce, whereby no transgression on the part of the spouse is required to be proven, or to no-fault divorce settlements, in which fault is not taken into account in the division of marital property. These laws were largely implemented from the 1950’s to the early 1970’s.)

There have been contradictory findings regarding the correlation between unilateral divorce laws and divorce rates. Peters (1986) using cross-sectional data determined that women in unilateral divorce states were no more likely to be divorced than women in mutual consent states. Friedberg (1998) found a positive effect of unilateral divorce on divorce rates using panel data, although Wolfers (2003) argues that the effect on divorce rates was a) short term, and b) endogenous as far as divorce trends in the states were already concerned. Gruber (2000) finds a highly significant impact of unilateral divorce on the likelihood of being divorced.

Gruber also points out, however, that there are other channels through which unilateral divorce affects child outcomes, including through decreasing the rate of separation vs. divorce, through increasing rates of marriage and through changing the bargaining power within marriage.

6This variation would be less than exogenous if it reflected divorce trends already existent in the state, and resulted from some growing demand for divorce, as is claimed by Wolfers (2003).

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For these reasons he claims that unilateral divorce laws are not an appropriate instrument for divorce.

Antecol & Bedard (2007) and Fertig (2004) use unilateral or no-fault divorce as an instrument not for divorce per se, but for the time spent living with a parent in childhood.

Antecol & Bedard (2007) use data from the National Longitudinal Survey of Youth to examine the effect of family structure on teenage drug use, crime and promiscuity. They use the number of years since age 21 that the mother has lived in a state with unilateral divorce laws to instrument for the number of months that the biological father lived with the child. They are satisfied that they have a relevant instrument because at the first stage the instrument is always individually significant at the one percent level, with the first stage F-statistics falling between 8 and 11, depending upon the youth behavior being estimated.

Fertig (2004) instruments for years spent with a biological father present using a child’s years of exposure to no-fault divorce. Her study used data from the core sample of the Panel Study of Income Dynamics, examining children born between 1948 and 1968. (She uses at least one of the parent’s marriage history files to determine the years of parental presence. It is not clear how she determined states of residence prior to 1968, the first year of the PSID.) Fertig determines that the stage coefficients for the instrument behave appropriately and the first-stage F-statistic is 16.17.

60 B.2 Applicability to This Paper

As stated above, modeling the underlying divorce process is outside the bounds of this study, and longitudinal approaches to controlling for family unobservables are not feasible given that key elements of the data are from a one-year Time and Transfers Supplement to the PSID.

It might be possible to take the approach of Lang and Zagorsky (2000) and others, to use not divorce, but time spent in childhood living with one or both parents and control for family unobservables using siblings. My sample, however, is of adults whose parents may well have split up after the children were grown. Also, I am interested in the relationship between transfers and divorce per se, and not death, military absences or temporary separations. Examining how co-residence with parents in childhood is related to transfers later in life could be an interesting question for another paper, however. (It is also true that using the retrospective marital history files of the parents of the sample members to construct these measures would have forced me to severely limit my sample size due to the incomplete nature of those files.)

This leaves me with the instrumental variables approach. First, as stated in the body of the paper, I not only have to instrument for divorce, but at the same time instrument for father’s and mother’s remarriage. This is not feasible, but just for the sake of argument, let’s say I drop the other endogenous variables (mother’s remarriage, father’s remarriage, AND, not knowing the whereabouts of the father or mother which also perfectly predict divorce) and only look at divorce.

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A suitable instrumental variable is one that is both relevant, meaning correlated with the endogenous variable⁷, and exogenous, meaning uncorrelated with the error term. Various papers have used unilateral or no-fault divorce, as already mentioned. Upon the suggestions of

colleagues, I have tried various other instruments, none of which have previously been shown in the literature to be suitable. Religiosity, for example, was shown unrelated to the increase in divorce rate when analyzed together with the adoption of no-fault divorce. (Nakonezny, Shull and Rodgers, 1995)

In this data set, however, a suitable variable may exist. I attempt to use several, including the implementation of unilateral divorce laws⁸, the implementation of no-fault divorce laws⁹, non-membership in the Catholic church¹⁰ degree of church attendance¹¹, whether the first-born child of the mother of the family was female and educational heterogamy¹² as defined by Manski, et al (1992).

For my sample (unmarried heads of household with at least one parent who is also a PSID sample member), I find the following correlations:

Correlation Divorced parents

Years in unilateral state 0.117

Years in no-fault state -0.055

Non-catholic 0.144

7Stock and Watson (2002) suggest a rule of thumb for a relevant instrument to be an F-statistic of at least 10 in the first-stage regression. (Chapter 10.)

8The number of years that the family would have lived in a unilateral state by 1988 assuming they stayed in their state of residence in 1968.

9 The number of years that the family would have lived in a no-fault state by 1988 assuming they stayed in their state of residence in 1968.

10 The family’s religion is first asked in the PSID in 1970. Being a self-described non-Catholic in 1970 is the variable.

11 Asked first in the PSID in 1970, this variable describes levels of church attendance from 1-lowest to 3-highest.

12Mother’s level of education> father’s level of education.

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Religious attendance -0.089

Educational heterogamy -0.083

Because I am instrumenting for a dichotomous endogenous variable within an OLS regression, I use the CDSIMEQ command in Stata (documented in Keshk, 2003). The only instrument that I find to have significance in the first stage probit regression is the years lived in a no-fault state. This is somewhat curious, given that its correlation is the lowest of all the

variables I tried. In the second stage the instrumented variable for divorce is insignificant, (with a positive coefficient, however) indicating that it has no effect on the transfer amount for those who receive a transfer. The insignificance is not surprising given that standard errors in two-stage models are very high. I only include this result as an exploration of potential instrumental variables, as I believe the true model must include the remarriage variables. Given the lack of control for unobserved family characteristics, the empirical results for divorce and remarriage in this paper must be viewed as correlations only, not as evidence of causality.

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